Happy Wednesday friends,

Today, we'll get started with the design verifications of timber shear connections.

In this article, we'll cover the shear capacity of nails.

Let's get into it..

The 4 Steps To Calculate The Shear Capacity of Nails According To Eurocode

In general we separate 2 types of shear connections in timber design:

• timber-timber connections and
• timber-steel connections

We already covered all verification formulas of the different failure modes of EN 1995-1-1 (8.6), (8.7), (8.9)-(8.13) in episode #23. You can check out the episode here.

In today's episode we'll run through the formulas of a single steel-to-timber nailed connection. If you want to see the formulas of a timber-to-timber/panel applied on a real building then you can check out Module #2: Structural Design of a Residential Timber Roof. In the e-book, I show you exactly how to verify the connection between OSB boards and rafters. The connection needs to resist the horizontal shear forces of the roof diaphragm but also the vertical suction wind loads.

Here's the example we use in today's tutorial. In real projects a single shear steel-to-timber nail connection is used to connect beam shoes to primary timber beams.

Step #1: Define the geometrical properties of the nail and timber elements

The elements have the following dimensions:

• Steel plate thickness: t_s=10mm
• Timber element: t_t=160mm
• Nail length: l_n=90mm
• Pointside penetration thickness: t₁=l_n-t_s=80mm
• Nail diameter d=3.4mm
• Nail head diameter d_h=8.5mm

Step #2: Define the material properties of the timber elements

Here are the strength and stiffness properties that we need in the calculation:

• Tensile strength of the wire (nail): f_u=600 N/mm²
• Density timber element: ρ_k=350 kg/m³

The partial safety factor is found in EN 1995-1-1 Table 2.3 as:

γ_M = 1.3

The beam is classified according to EN 1995-1-1 2.3.1.3 as service class 2 (assumption in this tutorial).

Then we'll verify the timber beam for a design load of load duration class short-term (EN 1995-1-1 Table 2.1) which leads to a modification factor (EN 1995-1-1 Table 3.1) of:

k_mod = 0.9

Step #3: Calculate the loads acting on the nail

In this step we need to calculate the characteristic loads that act on the connector. The characteristic area loads are applied to the slabs like the OSB board, transfered to the beams and then to the connection.

We won't show how to calculate the loads and how to do the load transfer in this newsletter, as each calculation of the individual load is an article for itself and load transfer is also a big topic. But if you want to learn load tranfer with a real building project then you can check out Module #2: Structural Design of a Residential Building.

In this email, we'll verify one nail for the following point load/ shear force.

V_d = 0.65 kN

Step #4: Shear design verification of the nail

First, we'll calculate the embedment strength of the timber element.

Characteristic embedment strength for the timber element (EN1995-1-1 (8.15)):

f_h.k.1 = (0.082 ⋅ ρ_k ⋅ d^-0.3) N/mm² = 19.9 N/mm²

Yield moment for round nails (EN1995-1-1 (8.14)):

M_y.Rk = 0.3 ⋅ f_u ⋅ d^2.6 = 4336.3 Nmm

Withdrawal resistance of the nail (EN1995-1-1 (8.25)):

f_ax.k = 20 ⋅ 10^-6 (ρ_k/(kg/m³))² N/mm² = 2.45 N/mm²

Pull-through resistance of the nail (EN1995-1-1 (8.26)):

f_head.k = 70 ⋅ 10^-6 (ρ_k/(kg/m³))² N/mm² = 8.6 N/mm²

Characteristic axial resistance for smooth nails (EN1995-1-1 (8.23)). If you are using a smooth nail, then use formulas EN 1995-1-1 (8.24):

F_ax.Rk = min(f_ax.k ⋅ d ⋅ t₁; f_ax.k ⋅ d ⋅ t_s + f_head.k ⋅ d_h²) = 0.66 kN

Steel-to-timber connections according to EN1995-1-1 8.2.2 (single shear)

EN1995-1-1 (8.9a):

F_v.Rk.a = 0.4 ⋅ f_h.k.1 ⋅ t₁ ⋅ d = 2.16 kN

EN1995-1-1 (8.9b):

F_v.Rk.b = 1.15 ⋅ √(2 ⋅ M_y.Rk ⋅ f_h.k.1 ⋅ d) + F_ax.Rk/4 = 1.05 kN

EN1995-1-1 (8.9c):

F_v.Rk.c = f_h.k.1 ⋅ t₁ ⋅ d ⋅ (√(2 + (4 ⋅ M_y.Rk)/(f_h.k.1 ⋅ d ⋅ t₁²)) – 1) + F_ax.Rk/4 = 2.48 kN

EN1995-1-1 (8.9d):

F_v.Rk.d = 2.3 ⋅ √(M_y.Rk ⋅ f_h.k.1 ⋅ d) + F_ax.Rk/4 = 1.41 kN

EN1995-1-1 (8.9e):

F_v.Rk.e = f_h.k.1 ⋅ t₁ ⋅ d = 5.41 kN

Characteristic shear capacity:

F_v.Rk = min(F_v.Rk.a; F_v.Rk.b; F_v.Rk.c; F_v.Rk.d; F_v.Rk.e) = 1.05 kN

Design withdrawal capacity:

F_v.Rd = k_mod ⋅ F_v.Rk/γ_M = 0.72 kN

Verification:

η = W_d/F_v.Rd = 0.90

Final Words

Alright, this is how you verify a steel-to-timber connection for shear according to Eurocode.

I hope this helped.

Enjoy the rest of the week and your weekend.

Let’s design better structures together,

Laurin.

P.S. If you want to learn more, here are a few ways I can help you:

#1: I teach you everything you need to know about load calculation. It's the most important fundamental of structural engineering. ​Without knowing the loads of a building, you can't design the structural elements. Click → here ← to learn.

#2: Previous episodes of the timber design series:

• Ep. #1: Welcome to the timber design series (click here)
• Ep. #2: Timber material properties (click here)
• Ep. #3: Tension verification of timber (click here)
• Ep. #4: Compression verification of timber (click here)
• Ep. #5: Bending verification of timber (click here)
• Ep. #6: Compression perpendicular to the grain (click here)
• Ep. #7: Shear verification (click here)
• Ep. #8: Deflection verification (click here)
• Ep. #9: Torsion verification (click here)
• Ep. #10: Lateral torsional buckling (click here)
• Ep. #11: Timber beam design (here)
• Ep. #12: Timber column design (here)
• Ep. #13: Vibration analysis of timber floors (here)
• Ep. #14: Timber joist floor (here)
• Ep. #15: CLT floor (here)
• Ep. #16: Timber stud walls (here)
• Ep. #17: CLT walls (here)
• Ep. #18: Timber Connection Design (here)
• Ep. #19: Tensile capacity of nails (here)
• Ep. #20: Tensile capacity of screws (here)
• Ep. #21: Tensile capacity of bolts (here)
• Ep. #22: Tensile capacity of staples (here)
• Ep. #23: Shear capacity of timber connections (here)

#3: The reinforced concrete series (click here)

#4: The engineering mechanics series (click here)

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